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variants of this functions
LegendreQ




Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreQ[nu,z] > Specific values > Specialized values > For fixed z





http://functions.wolfram.com/07.10.03.0015.01









  


  








Input Form





LegendreQ[9, z] == (1/80640) (-2 (16384 + 165 z^2 (-3867 + 91 z^2 (249 - 455 z^2 + 255 z^4))) - 315 z (315 + 11 z^2 (-420 + 13 z^2 (126 - 180 z^2 + 85 z^4))) (Log[1 - z] - Log[1 + z]))








Standard Form





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MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <semantics> <mi> Q </mi> <annotation encoding='Mathematica'> TagBox[&quot;Q&quot;, LegendreQ] </annotation> </semantics> <mn> 9 </mn> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 80640 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 165 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 91 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 255 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 455 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 249 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 3867 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 16384 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 315 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 11 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 13 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 85 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 180 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 126 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 420 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 315 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LegendreQ </ci> <cn type='integer'> 9 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 80640 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 165 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 91 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 255 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 455 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 249 </cn> </apply> </apply> <cn type='integer'> -3867 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 16384 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 315 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 11 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 13 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 85 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 180 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 126 </cn> </apply> </apply> <cn type='integer'> -420 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 315 </cn> </apply> <apply> <plus /> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LegendreQ", "[", RowBox[List["9", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List["16384", "+", RowBox[List["165", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3867"]], "+", RowBox[List["91", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["249", "-", RowBox[List["455", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["255", " ", SuperscriptBox["z", "4"]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List["315", " ", "z", " ", RowBox[List["(", RowBox[List["315", "+", RowBox[List["11", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "420"]], "+", RowBox[List["13", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["126", "-", RowBox[List["180", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["85", " ", SuperscriptBox["z", "4"]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["1", "-", "z"]], "]"]], "-", RowBox[List["Log", "[", RowBox[List["1", "+", "z"]], "]"]]]], ")"]]]]]], "80640"]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29